Suppose the functions $$ f, g, h $$ and $$ l $$ are defined as follows: $$ \begin{aligned} f(x) & =4 x^{2}-5 x+1 \ g(x) & =2 \sqrt{2-\frac{x}{2}}-x \ h(x) & =-\frac{1}{2} x+3 \ l(x) & =\log _{4}(x+3)-\log _{4}(x-2)\end{aligned} $$ $$ \begin{array}{l}\text { Solve the equation } g(x)=-4\end{array} $$

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To solve the equation $$ g(x) = -4 $$ where $$ g(x) = 2 \sqrt{2 - \frac{x}{2}} - x $$, follow these steps:

1. **Set Up the Equation:**
   $$
   2 \sqrt{2 - \frac{x}{2}} - x = -4
   $$

2. **Isolate the Square Root:**
   $$
   2 \sqrt{2 - \frac{x}{2}} = x - 4
   $$

3. **Determine the Domain:**
   - The expression inside the square root must be non-negative:
     $$
     2 - \frac{x}{2} \geq 0 \implies x \leq 4
     $$
   - Additionally, since the left side is non-negative, $$ x - 4 $$ must also be non-negative:
     $$
     x - 4 \geq 0 \implies x \geq 4
     $$
   - Combining these, the only possible value is $$ x = 4 $$.

4. **Verify the Solution:**
   Substitute $$ x = 4 $$ into the original equation:
   $$
   g(4) = 2 \sqrt{2 - \frac{4}{2}} - 4 = 2 \sqrt{0} - 4 = -4
   $$
   This satisfies the equation.

**Conclusion:**
The only solution to the equation $$ g(x) = -4 $$ is:

$$
\boxed{4}
$$
The solution to the equation $$ g(x) = -4 $$ is $$ x = 4 $$.

Suppose the functions and are defined as follows:

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